Geometry Problem 1459: Two Triangles, Orthocenter, Midpoint, Perpendicular

The figure shows the vertical angles BAC and DAE. F and G are the orthocenters of trianglers ABC and ADE, respectively. If M and N are the midpoints of BE and CD, respectively, prove that MN and FG are perpendicular.


Static Diagram of problem 1459

Dynamic Geometry 1459: Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration. Using GeoGebra


Poster of the problem 1459 using iPad Apps

Poster of Problem 1459, Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration, GeoGebra, iPad

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

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